An Introduction to Riemann-Finsler Geometry

PRELIMINARY TEXT. DO NOT USE. Finsler geometry is a metric generalization of Riemannian geometry and has become a comparatively young branch of differential geometry. Although Finsler geometry has its genesis in Riemanns 1854 "Habilitationsvortrag," its systematic study was not initiated until 1918 by Finsler, and the fundamentals were not completely formulated until the mid-thirties. Later, however, the field underwent a rapid development by mathematicians and physicists of many countries. The main purpose of this book is to study the metric geometry of Finsler manifolds. Portions of the book generalize some standard concepts from Riemannian geometry to the Finsler setting, while other